Definition df-csb 2006

Description: Define the proper substitution of a class for a set into another class. The underlined brackets distinguish it from the substitution into a wff, wsbc 1172, to prevent ambiguity. Theorem sbcel1g 2017 shows an example of how ambiguity could arise if we didn't use distinguished brackets. Theorem sbccsbg 2026 recreates substitution into a wff from this definition.

Assertion

Ref	Expression
df-csb	|- [_A / x]_B = {y | [A / x]y e. B}

Distinct variable groups:   y,A   y,B   x,y

Detailed syntax breakdown of Definition df-csb

Step	Hyp	Ref	Expression
1		vx	. . 3 set x
2		cA	. . 3 class A
3		cB	. . 3 class B
4	1, 2, 3	csb 2005	. 2 class [_A / x]_B
5		vy	. . . . . 6 set y
6	5	cv 957	. . . . 5 class y
7	6, 3	wcel 960	. . . 4 wff y e. B
8	7, 1, 2	wsbc 1172	. . 3 wff [A / x]y e. B
9	8, 5	cab 1466	. 2 class {y | [A / x]y e. B}
10	4, 9	wceq 958	1 wff [_A / x]_B = {y | [A / x]y e. B}

This definition is referenced by:  csbeq1 2007  csbid 2009  csbcog 2011  csbexg 2012  csbconstgf 2014  sbcel12g 2015  sbceqdig 2016  csbvarg 2025  hbcsb1g 2028  hbcsbg 2030  csbiegft 2033  csbabg 2047  fsump1f 7018

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